Question

Triangle ABC is similar to triangle LMN by the AA Similarity Postulate.

Also, m∠A = 108° and m∠C = 2(m∠M).

What is m∠M?

_________ °

Answer 1

A triangles angles have to add up to 180 degrees. So, 180-108= 72. 72/3=24m∠A=108 m∠C= 48 m∠M=24

108+48+24=180

Answer 2

m∠M=24°

Explanation:

The sum of all the angles of the triangle is equal to 180°. It is given that Triangle ABC is similar to triangle LMN by the AA similarity postulate, therefore, similar triangles have similar set of angles. If ∠A=108°, then ∠L will also be equal to 108°, ∠B=∠M and ∠C=∠N by similarity of the triangles.

Now, let ∠M=x, then ∠B=x, also it is given that ∠C=2∠M, therefore by the sum property of the triangles,

∠A+∠B+∠C=180°

⇒108°+x+2x=180° (because ∠C=2∠M=2x)

⇒3x+108°=180°

⇒3x=180°-108°

⇒3x=72°

⇒x=24°

Therefore, m∠M=24°